Derickx–van Hoeij conjecture on modular units computing the gonality of X_1(p)

Let $p$ be a prime, and let $X_1(p)$ denote the modular curve of level $p$. A modular unit is a function on $X_1(p)$ whose zeros and poles are cusps.

Derickx–van Hoeij conjecture. There is a modular unit $f$ defined over $\mathbb{Q}$ on $X_1(p)$ such that

$$\operatorname{gon}_{\mathbb{Q}}(X_1(p))=\deg f.$$

For primes up to the range studied by Derickx and van Hoeij, the rational gonality is achieved by a modular unit. The conjecture proposes that this remains true for every prime $p$.